Angle between velocity vectors of 2D billiard ball collision?

In summary, during a game of billiards, a white cue ball traveling at a velocity of v strikes a green ball at rest. After the collision, the green ball's velocity is twice that of the white ball's velocity. The angle between the cue ball's final velocity vector and the cue ball's initial velocity vector is 45 degrees. This is determined by using the equation v^2 = v_1^2 + v_2^2 and considering the elastic collision between the balls, which results in the construction of a right triangle with the initial velocity as the hypotenuse.
  • #1
naianator
48
1

Homework Statement


During a game of billiards, a white cue ball traveling at speed v strikes a green ball that was initially at rest. The green ball's speed after the collision is twice the speed of the white ball after the collision. The billiard balls have equal mass.

What is the angle between the cue ball's final velocity vector and the cue ball's initial velocity vector? (Enter an angle between 0 and 90 degrees.)

Homework Equations


v^2 = v_1^2+v_2^2

v = v_1+v_2

The Attempt at a Solution


I have determined that the speed of the cue ball after hitting the green ball is v/sqrt(5) making the speed of the green ball 2v/sqrt(5). From what I can tell cos(theta) = speed of cue ball after striking green ball/initial speed = v/sqrt(5)/v = 1/sqrt(5). But obviously this isn't correct. What am I doing wrong?
 
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  • #2
What is the exact question ? What kind of collision takes place ?

Hint : Does this even seem possible ( Compare KEf and KEi ) ?
 
  • #3
Qwertywerty said:
What is the exact question ? What kind of collision takes place ?

Hint : Does this even seem possible ( Compare KEf and KEi ) ?
I'm not sure what you mean... v^2 = v^2/5+4v^2/5 = v^2
its an elastic collision implying that the balls take off perpendicular to each other so I can construct a triangle
 
Last edited:
  • #4
naianator said:
I'm not sure what you mean... v^2 = v^/5+4v^2/5 = v^2
its an elastic collision implying that the balls take off perpendicular to each other so I can construct a triangle
naianator said:
The green ball's speed after the collision is twice the speed of the white ball after the collision.
Sorry , this seemed a bit confusing .

Okay , anyways , your answer is correct . However , what do you mean by ' constructing a triangle ' ?
 
  • #5
Qwertywerty said:
Sorry , this seemed a bit confusing .

Okay , anyways , your answer is correct . However , what do you mean by ' constructing a triangle ' ?
a right triangle of the velocity vectors - initial velocity being the hypotenuse... Is that correct? Anyhow, I'm not sure how I got the wrong answer before - must have been a calculator error. Thanks!
 
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What is a 2D billiard ball collision?

A 2D billiard ball collision is a physical event in which two billiard balls come into contact with each other in a two-dimensional space, causing a transfer of energy and momentum between them. This type of collision is commonly observed in the game of billiards or pool.

How do you calculate the outcome of a 2D billiard ball collision?

The outcome of a 2D billiard ball collision can be calculated using the laws of conservation of energy and momentum. These laws state that the total energy and momentum of a system must remain constant before and after a collision. By applying these laws along with the principles of elastic or inelastic collisions, the final velocities and directions of the balls can be determined.

What factors affect the outcome of a 2D billiard ball collision?

The outcome of a 2D billiard ball collision can be affected by various factors such as the masses and velocities of the balls, the angle at which they collide, and the type of collision (elastic or inelastic). Other factors such as the friction and spin of the balls may also play a role in the outcome of the collision.

Can a 2D billiard ball collision be perfectly elastic?

Yes, a 2D billiard ball collision can be perfectly elastic, meaning that the total kinetic energy of the system is conserved before and after the collision. This type of collision is achieved when there is no loss of energy due to friction or other external forces, and the balls are perfectly round and rigid.

How is a 2D billiard ball collision different from a 3D collision?

A 2D billiard ball collision occurs in a two-dimensional space, while a 3D collision occurs in a three-dimensional space. This means that in a 2D collision, the balls are restricted to move in a flat plane, while in a 3D collision, they can move in any direction within a three-dimensional space. The calculations for the outcomes of these collisions also differ due to the different number of dimensions involved.

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